The following plenary lectures are planned for the International Conference on Complementarity, Duality, and Global Optimization in Science and Engineering Conference
Duality: Gil Strang (Massachusetts Institute of Technology)
Complementarity: Jong-Shi Pang (Rensselaer Polytechnic Institute)
Global Optimization: Panos M. Pardalos (University of Florida)
Dual Problems of Mechanics in L^1 and L^Infinity
Gil Strang
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
Laplace's equation comes from minimizing the L^2 norm of grad u.Ê We consider the corresponding proglems in L^1 and L^infinity over a plane domain. We may minimize the norm of grad u subject to boundary conditions, or we may minimze the distance between grad u and a given vector field v (x,y). Of these four problems, some can be solved explicitly (with connections to a continuous max flow-min cut theorem). The problems have equivalent forms, using duality - and also using the fact that div w = 0 has the known general soution w = (s_y, -s_x) for some stream function s(x,y).
Some of our problems have explicit solutions. Others are unsolved.
Linear Complementarity Systems
Jong-Shi Pang, Department of Mathematical Sciences and
Department of Decision Sciences and Engineering Systems, Rensselaer
Polytechnic Institute, Troy, New York 12180-3590, U.S.A.
Email: pangj@rpi.edu.
Abstract. A linear complementarity system (LCS) is a piecewise linear
dynamical system consisting of a linear time-invariant ordinary
differential equation parameterized by an algebraic variable that is
required to be a solution to a finite-dimensional linear complementarity
problem whose constant vector is a linear function of the differential
variable. In this talk, we will formally define the LCS, explain its
importance in piecewise linear system theory, identify several
fundamental issues associated with such a nonsmooth system, and present
recent results that address these issues. Time permitting, we will
discuss extensions to nonlinear complementarity systems and to
differential variational inequalities.
Recent Developments in Multilevel Optimization
Panos M. Pardalos
Center for Applied Optimization, ISE Department
303 Weil Hall, University of Florida
PO Box 116595
Gainesville, FL 32611-6595
pardalos@ufl.edu
http://www.ise.ufl.edu/pardalos
In many decision processes there is a hierarchy of decision makers and decisions
are taken at different levels in this hierarchy. Multilevel Optimization focuses
on the whole hierarchy structure. The field of multilevel optimization has become
a well known and important research field. Hierarchical structures can be found in
scientific disciplines such as environment, ecology, biology, chemical engineering,
mechanics, classification theory, databases, network design, transportation, supply
chain, game theory and economics. In this talk we are going to survey recent
developments in the field and discuss a wide spectrum of applications.
